Find bit strings with no pairwise XOR sums in common; see https://math.stackexchange.com/questions/4624075.

Question4624075.java

import java.util.Random;

public class Question4624075 {
    final static int k = 34;
    final static int n = 10;
    final static int m = 1 << n;
    final static int nvalues = (k * (k + 1)) / 2;
    
    final static Random random = new Random();

    static int sum;
    static int min;
    static int count;
    static int [] counts = new int [m];
    static boolean [] used = new boolean [m];
    static int [] x = new int [k];

    static double beta;
    
    static void increment (int x) {
        sum += 2 * counts [x] + 1;
        if (++counts [x] == 2)
            count++;
    }
    
    static void decrement (int x) {
        sum -= 2 * counts [x] - 1;
        if (counts [x]-- == 2)
            count--;
    }

    static void clear (int i) {
        used [x [i]] = false;
        decrement (x [i]);
        for (int j = 0;j < k;j++)
            if (j != i)
                decrement (x [i] ^ x [j]);
    }
    
    static void set (int i) {
        used [x [i]] = true;
        increment (x [i]);
        for (int j = 0;j < k;j++)
            if (j != i)
                increment (x [i] ^ x [j]);
    }
    
    static void randomize (int i) {
        do
            x [i] = random.nextInt(m - 1) + 1;
        while (used [x [i]] || counts [x [i]] != 0);
    }
    
    public static void main (String [] args) {
        used [0] = true;
        
        for (int i = 0;i < k;i++) {
            randomize (i);
            used [x [i]] = true;
            increment (x [i]);
        }
        
        outer:
        for (int a : x)
            for (int b : x) {
                if (b == a)
                    continue outer;
                increment (a ^ b);
            }
        
        int l = 0;
        min = count;
        
        for (beta = 0;count > 0;beta += .00000008) {
            for (int i = 0;i < k;i++) {
                int oldSum = sum;
                int oldX = x [i];
                clear (i);
                randomize (i);
                set (i);
                if (sum > oldSum && Math.random() > Math.exp(beta * (oldSum - sum))) {
                    clear (i);
                    x [i] = oldX;
                    set (i);
                }
                min = Math.min(min,count);
            }

            if ((++l & 0x7fff) == 0)
                print();
        }
        
        print();
        
        for (int i = 0;i < k;i++) {
            System.out.print((i % 5) == 0 ? "\n" : " ");
            System.out.print(String.format("%" + n + "s", Integer.toBinaryString(x [i])).replace(' ', '0'));
        }
    }

    static void print() {
        System.out.println(beta + " : " + min + " / " + count + " / " + sum + " / " + nvalues);
    }
}